Solve for $x$ : $ 5|x - 10| + 3 = 4|x - 10| + 2 $
Answer: Subtract $ {4|x - 10|} $ from both sides: $ \begin{eqnarray} 5|x - 10| + 3 &=& 4|x - 10| + 2 \\ \\ { - 4|x - 10|} && { - 4|x - 10|} \\ \\ 1|x - 10| + 3 &=& 2 \end{eqnarray} $ Subtract ${3}$ from both sides: $ \begin{eqnarray} 1|x - 10| + 3 &=& 2 \\ \\ { - 3} &=& { - 3} \\ \\ 1|x - 10| &=& -1 \end{eqnarray} $ Simplify: $ |x - 10| = -1$ The absolute value cannot be negative. Therefore, there is no solution.